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Can’t wait to see how you’re gonna do the ref! ahahah
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How do you map the positions to a single number? Are you planning on using a space-filling curve?
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23 x 3, you'll want an x,y,z coordinate for each of them.
Can probably get away with 22x2 + 3 as I'm not sure the z coordinate is necessary for the players if you let them carry around a height and vertical attribute
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you probably need the momentum vector of each object too, so 23x6
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soccer should probably be modeled by a continuous time recursive bellman equation with a 23x3 dimensional state space (positions of 22 players plus position of the ball)